Lie algebra bundle associated to a Lie group bundle I was reading  the paper Non abelian Differentiable gerbes (page 24) and came across notion of Lie algebra bundles associated to a Lie group bundle.
I am not comfortable with these notions and google gave http://www.pphmj.com/Images/PT11.pdf which says

In 1966, A. Douady and M. Lazard constructed a Lie group bundle $\Gamma$ (not necessarily Hausdorff) for a given Lie algebra bundle $\xi$ such that the Lie algebra bundle of a Lie group bundle $\Gamma$ is isomorphic to a given Lie algebra bundle $\xi$ in their remarkable paper.

The paper they have mentioned is 

A. Douady and M. Lazard, Espaces fibres en algebre de Lie et en groupes, Invent. Math. 1 (1966), 133-151. (digizeitschriften)

I do not read that language. 
Can some one give a reference in English where this result is discussed, briefly atleast.
I am guessing that  Lie algebra bundle  over a manifold $M$ associated to a Lie group bundle over a manifold $M$ should be something where each fibre of $x\in M$  is Lie algebra $\mathfrak{g}_x$ of Lie group $G_x$ which is fibre of $x$ of Lie group bundle.
Any comments are welcome.
Edit : I assume the notion of group bundle is same as that of the paper Notes on 1-gerbes and 2-gerbes (because this paper is closely related to the paper Non abelian differentiable gerbes mentioned above). According to that paper the following is the definition of group bundle :

the standard notion of an $X$-group scheme $G$ will correspond in a topological context to that of a bundle of groups on a space $X$. By this we mean a total space $G$ above a space $X$ that is a group in the cartesian monoidal category of spaces over $X$. In particular, the fibers $G_x$ of $G $ at points $x \in X$ are topological groups, whose group laws vary continuously with $x$.

Thus, I consider the possibility that the fibers are not necessarily isomorphic. 
 A: Let me first discuss Lie algebra bundles. If I understand the question right, then we are given a smooth vector bundle $E\to M$ together with a fiber respecting smooth fiberwise bilinear mapping $[\;,\;]:E\times_M E \to E$ which is fiberwise a Lie algebra structure. The question now is: when is the Lie algebra isomorphism class of the Lie algebras $E_x$ locally constant on $M$? This is the case if the Lie algebra is rigid: This means that the orbit through the Lie algebra structure on $\mathbb R^n$ (the typical fiber) of $\operatorname{GL}(n)$ in $L^2_{\text{skew}}(\mathbb R^n\times \mathbb R^n,\mathbb R^n)$ under the action 
$(A,F)\mapsto A\circ F\circ (A^{-1}\times A^{-1})$ is open in the real subvariety of Lie algebra structures (i.e., also satisfying the Jacobi identity). Semisimple Lie algebras are rigid. Nilpotent and solvable ones are not, in general: These have real moduli which may change in a smooth way with $x\in M$. So the isomorphism class of the Lie algebra $E_x$ is locally constant in $M$ around a rigid Lie algebra $E_x$. 
By exponentiation this result carries over to fiber bundles with a smooth Lie group structure. 
For information on rigid Lie algebras see papers by Michel Goze.
One recent paper is:


*

*MR1868184  Goze, Michel; Ancochea Bermudez, Jose Maria. On the classification of rigid Lie algebras. J. Algebra 245 (2001), no. 1, 68–91   

A: Refer the paper by Basavavannappa S KIRANAGI(B S KIRANAGI) on Lie Algebra Bundles, Bull. Sci. Math.2 series, 102(1978), 57-62. there are many papers by him.
A: Are you familiar with the Lie algebroid associated to a Lie groupoid? A Lie group bundle is in particular a Lie groupoid $\Gamma \rightrightarrows M$ where the source and target maps are equal, and the associated Lie algebra bundle is the Lie algebroid of this Lie groupoid.
